Question

Use a graphing calculator to find the solution of the equation. Check your solution algebraically. $$0.7(3 x-20)=22-3.9 x$$

Short answer

The correct solution would be given by the x-coordinate of the point where the graph crosses the X-axis. The specific value needs to be calculated using a graphing calculator and then confirmed algebraically by plugging it into the original equation.

Step-by-step solution

Rearrange the equation

First, rearrange the equation to have both sides equal to zero. So, the given equation \(0.7(3x - 20) = 22 - 3.9x\) becomes \(0.7(3x - 20) + 3.9x - 22 = 0\).

Graph the equation

Next, plot the equation \(y = 0.7(3x - 20) + 3.9x - 22\) on the Y-axis of the graphing calculator. This gives you a visual representation of the equation.

Find the intersection point

Look for the point where the graph intersects the X-axis. This intersection represents the solution to the equation, as it is the value of x that makes the equation equal to zero.

Check solution algebraically

Finally, substitute the found value of x in the main equation to verify that it is indeed the solution. If the left-hand side equals the right side when the solution is substituted, then it is the correct answer.